The period the time required for one complete swing of a sim

The period (the time required for one complete swing) of a simple pendulum varies directly as the square root of its legnth. If a pendulum 12 feet long has a period of 4 seconds, find the period of a pendulum 3 feet long.

Solution

\"The period (the time required for one complete swing) of a simple pendulum varies directly as the square root of its legnth\"
___ P = k sqrt(L)

4 = k sqrt(12)

4 / sqrt(12) = k ___ 2 / sqrt(3) = k ___ 2 sqrt(3) / 3 = k


for a 3ft pendulum ___ P = k sqrt(3) = [2 sqrt(3) / 3] sqrt(3) = 2